Aircraft_perf_notes3

# Aircraft_perf_notes3 - Analysis of Air Transportation...

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Unformatted text preview: Analysis of Air Transportation Systems Fundamentals of Aircraft Performance (3) Dr. Antonio A. Trani Associate Professor of Civil and Environmental Engineering Virginia Polytechnic Institute and State University Fall 2004 Blacksburg NEXTOR - National Center of Excellence for Aviation Research 1 Computer Program to Estimate Aircraft Climb Performance • A computer model to estimate the climb performance of subsonic aircraft • Assumes a parabolic drag polar • Assumes a known velocity proﬁle during climb • A separate program ﬁle is created to specify the aircraft performance characteristics NEXTOR - National Center of Excellence for Aviation Research 2 Climb Performance Computer Program NEXTOR - National Center of Excellence for Aviation Research 3 File: Climb_segment_2003.m NEXTOR - National Center of Excellence for Aviation Research 4 Function: fclimb_04.m NEXTOR - National Center of Excellence for Aviation Research 5 Function: drag_03.m NEXTOR - National Center of Excellence for Aviation Research 6 Function: thrust_calculation.m NEXTOR - National Center of Excellence for Aviation Research 7 Aircraft Data File: boeing777_class.m NEXTOR - National Center of Excellence for Aviation Research 8 Example of Aircraft Climb Performance The following example gives an idea of the typical procedures in the estimation of the aircraft climbing performance. Assume that a heavy transport aircraft has drag polar of the form, C2 L C D = C Do + ------------π ARe where: AR = 8.7, e =0.87 and CDO (the zero lift drag coefﬁcient) varies according to true airspeed (TAS) according to the following table: Mach Number 0.0 to 0.75 0.80 CDO (nondimensional) 0.0180 0.0192 NEXTOR - National Center of Excellence for Aviation Research 9 Mach Number 0.85 0.90 0.95 1.00 CDO (nondimensional) 0.023 0.037 0.038 0.040 The engine manufacturer supplies you with the following data for the engines of this aircraft: True Mach Number 0 0.90 Sea Level Thrust (Newtons) 370,000 240,000 For simplicity assume that thrust variations follow a linear behavior between 0 and 0.90 mach. The thrust also decreases with altitude according to the following simple thrust lapse rate equation, Taltitude = TSea Level (ρ/ρο).90 NEXTOR - National Center of Excellence for Aviation Research (1) 10 where ρ is the density at altitude h and ρο is the sea level standard density value (1.225 kg./ m3). The aircraft in question has four engines and has a wing area of 440 m2. A) Calculate the thrust and drag for this vehicle while climbing from sea level to 10,000 m. under standard atmospheric conditions with a speed proﬁle shown below. Simulate the climb performance equation of motion assuming that the takeoff weight is 320,000 kg. Vclimb = [ 200 200 230 250 270 300 300 300 300 300 300 300 300 300 300]; % speed in knots (IAS) NEXTOR - National Center of Excellence for Aviation Research 11 altc = [ 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 12000 13000 14000]; % altitude for IAS in meters The fuel consumption is approximately proportional to the thrust as follows, Fc = TSFC (T) where: tsfc = 1.6e-4 is the thrust speciﬁc fuel consumption (N/N/s) B) Find the time to climb and the fuel consumed to 10,000 m. C) What is the approximate horizontal distance traveled to reach 10,000 m. altitude? NEXTOR - National Center of Excellence for Aviation Research 12 Solution • Set the initial conditions in the main program (climb_segment_2003.m) as follows: global g mass rhos hcruise % Enter aircraft ﬁle desired boeing777_class h_airport = 0; % airport altitude (m) rhos = 1.225; % sea level density (kg/m-m-m) hcruise =10000; % cruise altitude (m) Mass_init = mass*g; % Initial weight (Newtons) • The aircraft ﬁle called boeing777_class.m is used • The climb proﬁle is shown in the next pages NEXTOR - National Center of Excellence for Aviation Research 13 Climb Proﬁle Solution DTW = 320,000 kg. Variable climb speed NEXTOR - National Center of Excellence for Aviation Research 14 Analysis (Distance vs. Altitude Proﬁle) • The aircraft climb rate is high at low altitudes because the thrust developed by the engines is high compared with the drag forces • As the vehicle climbs higher, engine thrust developed is reduced and so does climb rate • The aircraft covers 250 kilometers to climb to 10,000 meters (33,000 ft.). • The ODE solver takes a few more iterations near the Top of Climb (TOC) to solve the differential equations of motion because the rates of change of the state variables change more drastically (specially in the neighborhood of the TOC when the aircraft levels off) NEXTOR - National Center of Excellence for Aviation Research 15 Climb Proﬁle Comparison (DTW Changes) DTW = 280,000 kg. DTW = 320,000 kg. DTW = 300,000 kg. NEXTOR - National Center of Excellence for Aviation Research 16 Analysis (Changes in Desired Takeoff Weight) • A heavier aircraft (DTW = 320,000 kg) climbs slower than a lighter aircraft (DTW = 280,000 kg) • The difference in climb distance is signiﬁcant (175 km for DTW=280,000 versus 250 km when DTW=320,000 kg) • The initial cruise altitude for a lighter aircraft is higher than that for a heavier aircraft (not shown in the diagram but can be easily demonstrated using the same program) NEXTOR - National Center of Excellence for Aviation Research 17 Climb Time Proﬁle DTW = 320,000 kg. Variable climb speed NEXTOR - National Center of Excellence for Aviation Research 18 Analysis (Climb Time Proﬁle) • The aircraft takes 1,000 seconds (17 minutes) to climb to 10,000 meters • A lighter aircraft reaches the TOC faster (using time as the metric) than a heavier aircraft NEXTOR - National Center of Excellence for Aviation Research 19 Aircraft Climb Proﬁle (Rate of Climb) DTW = 320,000 kg. Variable climb speed NEXTOR - National Center of Excellence for Aviation Research 20 Analysis (Rate of Climb) • The rate of climb diminishes with altitude gains • At higher altitudes the thrust produced by the engine is greatly reduced • The hysteresis observed near the TOC point is due to the small overshoot in altitude • The true airspeed during climb (in knots) is observed to increase with altitude. Note that by the time the aircraft reaches TOC the speed is near 440 knots • The aircraft weight changes substantially during climb (from 3,200,000 N at takeoff to near 3,070,000 N at TOC) NEXTOR - National Center of Excellence for Aviation Research 21 Aircraft Climb Proﬁle (Speed) DTW = 320,000 kg. Variable climb speed NEXTOR - National Center of Excellence for Aviation Research 22 Aircraft Climb Proﬁle (Aircraft Weight) DTW = 320,000 kg. Variable climb speed NEXTOR - National Center of Excellence for Aviation Research 23 Aircraft Climb Proﬁle (Thrust and Drag) DTW = 320,000 kg. Variable climb speed NEXTOR - National Center of Excellence for Aviation Research 24 Analysis (Thrust and Drag) • The thrust decrease substantially with altitude • The total drag remains near constant compared with thrust • At the TOC point, the aircraft has little climb capability because thrust and drag curves are close (little capability to climb) NEXTOR - National Center of Excellence for Aviation Research 25 ...
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## This note was uploaded on 12/31/2011 for the course CEE 5614 taught by Professor Staff during the Fall '10 term at Virginia Tech.

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